MinT - Best Known (41−19, 41, s)-Nets in Base 9

Best Known (41−19, 41, s)-Nets in Base 9

(41−19, 41, 200)-Net over F₉ — Constructive and digital

Digital (22, 41, 200)-net over F₉, using

1 times m-reduction [i] based on digital (22, 42, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 21, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(41−19, 41, 9025)-Net in Base 9 — Upper bound on s

There is no (22, 41, 9026)-net in base 9, because

1 times m-reduction [i] would yield (22, 40, 9026)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 147 816572 676491 031680 289372 920123 696529 > 9⁴⁰ [i]